Co-pending Italian Patent Application No. T091A000211, filed concurrently herewith by the Assignee of the present invention and which is incorporated herein in the interest of full disclosure, relates to a method and device for joining stratified or layered tire portions or components by means of an innerstitching operation, during which, the inner carcass of a green tire and the outer tread belt are assembled together inside a fixed stitching mold by rotating stitching devices over the inner surface of the carcass. The stitching devices push the carcass radially outwardly so as to adhere perfectly to the tread belt or ply, which in turn is pushed or reacts against the inner surface of the stitching mold in contact therewith thereby accurately forming the finished green tire.